It was Muller's first lesson in seemingly small things becoming big things when you are the Leader of the Opposition.
Other than the cap, those first days could not have gone better for Muller in introducing himself to the New Zealanders he wants to vote for him come September.
There were some minor rookie mistakes – falling into a trap of voicing a preference for Joe Biden over US President Donald Trump ahead of the US elections was one of them.
But Muller had that precious, precious commodity for his first days: clear air.
The leadership vote happened on a Friday and in a recess week.
That meant he had the weekend without interference to take his first steps.
Prime Minister Jacinda Ardern was taking a weekend off and did not appear in the media at all. That MAGA cap was the only thing to hog his limelight.
Muller needed the exposure – Muller was as a relative unknown to many people.
He also seemed to make a good fist of it, even the less formal appearances in the media.
A minefield lies ahead this week as he reshuffles his team of MPs and sets up his own office.
That is a tricky business: bringing in new people inevitably means demoting or getting rid of others.
Many Bridges' staff will quit or lose their jobs and emotions can run high.
The reshuffle will be more critical to get the caucus running smoothly. That is coming today.
Muller has sworn to do it on merit. If there is any perception he only deems his own supporters to have "merit" there will be trouble.
Things are sensitive in many quarters, and Muller will be hoping that does not last long.
He can take steps himself to ease it, in particular by being generous to those he has ousted.
If those who are ousted make that difficult for him, the other MPs will only punish them.
For Muller is right that there is no time for "brooding" with an election so close.
In that regard, a rip-snorting poll has remarkable healing properties.
Internal polls will arrive on Wednesday. Public polls will be a month or so later.
But Muller's solid performance and the public reaction MPs are reporting back on Muller's first days will be a good start.